1. Software version

MATLAB2021a

2. Part of the core code

clear all   
Nt=2;                                                        
co_time=2;                                                  
Nr=2;                                                              
Nit=1000;                                                        
M_psk=16;  

x=pi/6;
%x=0.5;
m=exp(j*x);
n=sqrt(m);

snr_min=0;                                                         
snr_max=20;                                                       
graph_inf_bit=zeros(snr_max-snr_min+1,2);                          
graph_inf_sym=zeros(snr_max-snr_min+1,2);                          
num_X=4;
num_bit_per_sym=log2(M_psk);                                     
co_x=zeros(num_X,1);
for SNR=snr_min:snr_max                                          
    clc
    disp('Wait until SNR=');disp(snr_max);
    SNR
    n_err_bit=0;
    graph_inf_bit(SNR-snr_min+1,1)=SNR;
    for con_sym=1:Nit                                               
       bi_data=randint(num_X,num_bit_per_sym);
        
        for i=1:4
           if bi_data(i,:)==[0 0 0 0]
                data(i,1)=3+3*j;
            elseif bi_data(i,:)==[0 1 0 0]
                data(i,1)=3+j;
            elseif bi_data(i,:)==[1 1 0 0]
                data(i,1)=3-j;
            elseif bi_data(i,:)==[1 0 0 0]
                data(i,1)=3-3*j;
            elseif bi_data(i,:)==[0 0 0 1]
                data(i,1)=1+3*j;
            elseif bi_data(i,:)==[0 1 0 1]
                data(i,1)=1+j;
            elseif bi_data(i,:)==[1 1 0 1]
                data(i,1)=1-j;
            elseif bi_data(i,:)==[1 0 0 1]
                data(i,1)=1-3*j;
            elseif bi_data(i,:)==[0 0 1 1]
                data(i,1)=-1+3*j;
            elseif bi_data(i,:)==[0 1 1 1]
                data(i,1)=-1+j;
            elseif bi_data(i,:)==[1 1 1 1]
                data(i,1)=-1-j;
            elseif bi_data(i,:)==[1 0 1 1]
                data(i,1)=-1-3*j;
            elseif bi_data(i,:)==[0 0 1 0]
                data(i,1)=-3+3*j;
            elseif bi_data(i,:)==[0 1 1 0]
                data(i,1)=-3+j;
            elseif bi_data(i,:)==[1 1 1 0]
                data(i,1)=-3-j;
            else data(i,1)=-3-3*j;
            end
        end
        H1=(randn(Nt,Nr)+j*randn(Nt,Nr))/sqrt(2);
        
        X1=zeros(co_time,Nt);
       
       % X1=[data(1,1)+data(2,1)  data(3,1)-data(4,1)
       %     data(3,1)+data(4,1)  data(1,1)-data(2,1)]; 
         X1=[data(1,1)+m*data(2,1)  n*(data(3,1)-m*data(4,1))
             n*(data(3,1)+m*data(4,1))  data(1,1)-m*data(2,1)];      
        
        snr_de=10^(SNR/10);
        sig=sqrt(Nt/snr_de);
        Noise1=sig*(randn(co_time,Nr)+j*randn(co_time,Nr))/sqrt(2);
        
        R1=H1*X1+Noise1;
        Noise2=reshape(Noise1,4,1);
        
        I=eye(2,2);
        H2=kron(I,H1);
        %M=[1 1 0 0
        %   0 0 1 1
        %   0 0 1 -1
        %   1 -1 0 0];
        M=[1  m  0  0
           0  0  n  m*n
           0  0  n -m*n
           1 -m  0  0];
        C=[data(1,1);data(2,1);data(3,1);data(4,1)];
        %C=[data(1,1);m*data(2,1);n*data(3,1);m*n*data(4,1)];
        R2=H2*M*C+Noise2;
        
        G=[real(H2*M) -imag(H2*M);imag(H2*M) real(H2*M)];
        CC=[real(C);imag(C)];
        Noise=[real(Noise2);imag(Noise2)];
        RR=G*CC+Noise;
        S=[real(data(1,1))
           imag(data(1,1))
           real(data(2,1))
           imag(data(2,1))
           real(data(3,1))
           imag(data(3,1))
           real(data(4,1))
           imag(data(4,1))];
        
        H=[G(:,1) G(:,5) G(:,2) G(:,6) G(:,3) G(:,7) G(:,4) G(:,8)];
        R=H*S+Noise;
        C1=(2*Nt)*(2/(10^(SNR/10)));
        codebook=[-3 -1 1 3];
        
        y_2norm_temp = spheredecodetoML(R, C1, H, codebook);
           
        rr=[y_2norm_temp(1)+j*y_2norm_temp(2)
            y_2norm_temp(3)+j*y_2norm_temp(4)
            y_2norm_temp(5)+j*y_2norm_temp(6)
            y_2norm_temp(7)+j*y_2norm_temp(8)];
        
      
       U=[0 0 0 0;0 1 0 0;1 1 0 0;1 0 0 0;0 0 0 1;0 1 0 1;1 1 0 1;1 0 0 1;0 0 1 1;0 1 1 1;1 1 1 1;1 0 1 1;0 0 1 0;0 1 1 0;1 1 1 0;1 0 1 0];
       X=[3+3*j;3+j;3-j;3-3*j;1+3*j;1+j;1-j;1-3*j;-1+3*j;-1+j;-1-j;-1-3*j;-3+3*j;-3+j;-3-j;-3-3*j];
       Dis=zeros(4,16);
       re_met_bit=zeros(4,4);
for a=1:4
    for b=1:16
        Dis(a,b)=abs(rr(a,1)-X(b,1))^2;
    end
[Dis,index]=sort(Dis,2);
re_met_bit(a,:)=U(index(a,1),:);
end
                
        for con_dec_ro=1:num_X                                            
            for con_dec_co=1:num_bit_per_sym
                if re_met_bit(con_dec_ro,con_dec_co)~=bi_data(con_dec_ro,con_dec_co)
                   n_err_bit=n_err_bit+1;
                end
            end
        end
    end
   
    Perr_bit=n_err_bit/(num_X*Nit*num_bit_per_sym);
    graph_inf_bit(SNR-snr_min+1,2)=Perr_bit;
end

x_bit=graph_inf_bit(:,1);
y_bit=graph_inf_bit(:,2);
semilogy(x_bit,y_bit,'g-o');
xlabel('SNR, [dB]');
ylabel('Bit Error Probability');
grid on